Process for separating upgoing and downgoing events on vertical seismic profiles

ABSTRACT

A process for separating upgoing and downgoing seismic wave events in a vertical seismic profile, and particularly for vertical seismic profiles wherein the seismic energy source is offset from the borehole in which seismic detectors are located in vertical spaced array. The process operates on two detector signals at a time (as S 1  and S 2 ) and is based on the concept that waves traveling in opposite directions have spatial derivatives of opposite sign. The derivative is approximated by the difference of the two signals which is time integrated to recover the phase. The resulting integrated difference signal I is then amplitude scale corrected and combined by addition or substraction with a signal S 0  representing the sum of the two detector signals to form a succession of filtered signals which, when recorded in alignment in order of detector depths to form a vertical seismic profile preserves either the upgoing or the downgoing seismic events.

FIELD OF THE INVENTION

This invention relates to a method of seismic surveying by the verticalseismic profile technique in which seismic wave detectors located in awell bore at different depths detect acoustic waves emanating from aseismic energy source located at or near the earth surface and generaterepresentative electrical signals in response thereto which are recordedin aligned array in order of detector depths, and more particularly to amethod for the processing of seismic data signals for separating thedowngoing wave events from the upgoing wave events on a vertical seismicprofile.

BACKGROUND OF THE INVENTION

Seismic surveying typically involves the use of a source of seismicenergy and an array of seismic detectors strategically positioned forits reception. The source of seismic energy can be an apparatus capableof delivering a series of impacts or mechanical vibrations to thesurface of the earth, the detonation of a high explosive charge near theearth surface, or other means capable of generating seismic wave energy.The resulting acoustic waves generated in the earth, including thosewhich are reflected from earth strata interfaces, are detected byseismic detectors which transduce the acoustic waves into representativeelectrical signals. From these electrical signals, informational datamay be deduced concerning the structure of earth's substrata.

In vertical seismic profiling, the seismic detectors are positioned atdifferent depths in a borehole, such as a well bore, and the signalsfrom the detectors in response to reception of energy from a seismicenergy source are recorded and grouped in alignment in a single displayin the order of detector depth. From this display, coherences betweenthe signal traces may be noted which may be analyzed and interpreted toprovide information regarding the geologic substructure. However,because of the multiplicity of components comprised in the seismicenergy received by a detector and its representative electrical signal,analysis of the signals is oftentimes exceedingly difficult. Suchcomponents will typically include a downgoing component representing thedirectly arriving wave field propagated from the energy source, otherdowngoing components from seismic energy which have undergone multiplereflections in geologic strata above the detector, upgoing componentsfrom seismic energy reflected from interfaces of geologic strata orstructures located below the detector, and spurious waves of variouskinds.

Heretofore, a number of field-operating and data processing techniqueshave been devised to accentuate the upgoing components in the detectorsignals and at the same time minimize the interfering effects of thedowngoing components since it is the upgoing components and theirtransit times representative of reflections from substrata interfaceswhich provide most useful information and are of primary concern. Mostof the current techniques for separating the opposite directions ofseismic wave travel in the detector signals assume that time shiftswhich align the first breaks in the signal traces can also be used toalign the desired upgoing seismic wave events. However, this assumptionis strictly true only where the upgoing events are derived fromhorizontal reflectors and the detector signals are from detectorslocated in a vertical borehole with zero source offset, i.e., theseismic source is located as close to the borehole as possible ratherthan being offset therefrom. In particular, the current techniques areof limited effectiveness in compensating for "dipping" reflectors and inoffset vertical seismic profiling used to identify geologicsubstructures, such as faults or salt domes located a distance from thewell bore. Also, the multichannel "dip" filters in current use generallyrequire many more than two detector signals from which to extractdesired information.

The new filtering process described herein does not requirepreprocessing to align seismic events in seismic signal traces and isapplicable to a wide range of geometries, including vertical seismicprofiling applications wherein the seismic source is offset from thewell bore. It also makes possible, by means of two-trace filtering, toreduce the number of receiver depth levels required in the acquisitionof a vertical seismic profile, and therefore a reduction in acquisitioncosts.

SUMMARY OF THE INVENTION

The invention relates to a method of seismic surveying by the verticalseismic profile technique which seismic detectors located in a well boreat different depths detect seismic wave energy emanating from a seismicenergy source located at or near the earth surface and generaterepresentative electrical signals in response thereto, which signals arerecorded in order of detector depths in a vertical seismic profile arrayand processed for separating the upgoing seismic wave events from thedowngoing seismic wave events. The process includes the steps ofcombining a pair of detector signals from adjacent levels in the wellbore to form a sum signal, subtracting the signal of the lower detectorof the pair from the signal of the other to form a difference signal,integrating the difference signal to form an integral signal,calculating and applying an amplitude scale correction to the integralsignal to approximate arrival times appropriate for a detector depthmidway between the detector pair, and subtracting the amplitudecorrected integral trace from the sum trace to thereby increase theamplitudes of the seismic events which are upwardly traveling as theyarrive at the detectors and attenuate the seismic events which aredownwardly traveling as they arrive at the detectors. The process stepsare successively applied two-by-two to all the signals in a verticalseismic profile to provide a modified vertical seismic profile whereinthe upgoing events are enhanced relative to the downgoing events. In analternate modification of the process which preserves the downgoingevents, the time corrected signal is added to the sum signal rather thansubtracted therefrom.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic illustration of an earth cross-sectionpenetrated by a well bore and the wave path geometry of seismic wavesemanating from a seismic energy source at the earth surface and receivedby a seismic detector located at a specified depth in the well bore;

FIG. 2 is a vertical seismic profile display of detector signalsrepresentative of seismic waves received over time by seismic detectorspositioned at successively greater depths in a well bore wherein thedetector signals are arranged in horizontal alignment in correspondencewith the depth of the detectors and the differing appearances ofdirectly arriving waves at the detectors and wave reflections frominterfaces of geologic strata located below the detectors areillustrated;

FIG. 3 is a reproduction of signal traces 10 and 11 in the verticalseismic profile of FIG. 2 where these traces are each displayed inhorizontal orientation and aligned one below the other;

FIG. 4 is a display, similar to FIG. 3, of sum and difference signaltraces representing the sum and difference of the pair of signal traces10 and 11 and a third signal trace, an integral trace, representing anintegration of the difference signal trace;

FIG. 5 is a display of a first signal trace resulting from thesubstraction of the integral trace from the sum trace and a secondsignal trace resulting from an addition of the integral trace and thesum trace;

FIG. 6 is a vertical seismic profile derived from the vertical seismicprofile of FIG. 2 after the process of the invention has been applied insuccessive steps, two traces at a time, to all the signal traces in thevertical seismic profile of FIG. 2;

FIG. 7 is a block diagram of a system according to the invention for thefiltering of detector signals obtained in the acquisition of a verticalseismic profile;

FIG. 8 is a diagrammatic illustration of the ray-path geometry of anincident wave approaching the axis defined by two seismic detectorspositioned at two adjacent levels in a well bore;

FIG. 9 is a graph in polar form representing the directional amplituderesponse, R(θ, θ_(o)), for the filtering process of the invention as afunction of incident angle wherein the directly arriving wave arrives atan incident angle of 0° with respect to the axis defined by the pair ofreceivers in FIG. 7;

FIG. 10 is a graph in polar form representing the directional amplituderesponse, R(θ, θ_(o)), for the filtering process of the invention as afunction of incident angle wherein the directly arriving wave arrives atan incident angle of 30° with respect to the axis defined by the pair ofreceivers in FIG. 7; and

FIG. 11 is a graph in polar form representing the directional amplituderesponse, R(θ, θ_(o)), for the filtering process of the invention as afunction of incident angle wherein the directly arriving wave arrives atan incident angle of 60° with respect to the axis defined by the pair ofreceivers in FIG. 7.

DESCRIPTION OF A PREFERRED EMBODIMENT

Referring to the drawings in greater detail, FIG. 1 illustratesschematically a typical arrangement of apparatus for conducting seismicoperations for the acquisition of a vertical seismic profile. A drillingrig 11 is shown in position over a well bore 13 which has been drilledin earth formations 15,16,17. The well bore 13 may be of any specifieddepth but typically extends to a depth of several thousand feet. Aseismic wave transducer or detector 19, sometimes called a geophone, issuspended on a conductor cable 21 in the well bore 13 at a predetermineddepth above the interfaces 22,23 of the earth strata 15,16 and 16,17respectively. The cable 21 which is wound about a reel 24 mounted on thedrilling rig 11 or located elsewhere on the earth surface near the wellbore 13, allows the transmission of electrical signals produced by thedetector 19 to surface equipment 25 for recording and processing. Suchequipment typically includes a means (not shown) for providing a preciseindication of the depth of the detector 19.

Also shown in FIG. 1 is a seismic wave source 34 located on the earthsurface 33 and offset from the well bore 13. The seismic wave source isdepicted in FIG. 1 as a weight-dropper 34 which is capable of dropping aweight to deliver a series of impacts to the earth, although it is to beunderstood, that various other seismic wave generating means, such as avibrator or explosive charge, could substitute therefor.

In operation, seismic waves are generated by an impact delivered by theweight-dropper 34 on the earth surface 33. These waves are propagated inthe earth formations below and detected by the detector 19 which isfastened against the wall of the well bore 13 by an anchoring element(not shown) in a manner providing contact between the detector and wallof the well bore which is suitable for the reception of seismic waveenergy. Such an anchoring element is shown in U.S. Pat. No. 4,397,004.In response to the detection of seismic wave energy, the geophone 19generates an electrical signal representative of the seismic wavesimpinging thereon and this signal is transmitted via the conductor cable21 to a magnetic recorder included in the surface equipment 25. Whileonly a single detector 19 is shown in FIG. 1, it is to be understoodthat a plurality of such detectors may be suspended on the cable 21 invertically spaced orientation in contact with the wall of the well boreand their signals transmitted via multiple conductors of the cable 21 tothe recording equipment which may be any conventional multitracerecorded suitable for recording the individual geophone output signalsin reproducible form.

It is to be noted from observation in FIG. 1 of the ray paths of seismicenergy emanating from the source 31, that some of the seismic waveenergy travels downwardly and directly to the detector 19 as indicatedby the ray path 41 and is normally the first seismic event to bedetected by the detector 19. However, there may be other seismic eventswhich are downwardly traveling as they impinge on the detector 19. Onesuch, as indicated by the ray path 43, may be a multiply reflected waverepresenting a portion of the seismic energy which strikes the geologicinterface 22 and is reflected thereby to reverberate between theinterface 22 and the earth surface 33. In addition, some of the seismicwave energy which is reflected by the interface 22 and illustrated bythe ray path 45 is upwardly traveling as it impinges on the detector 19and is the first upwardly traveling seismic event to be detected bydetector 19.

However, the downwardly traveling seismic wave energy which strikes theinterface 22 is not totally reflected therefrom and some of the seismicwave energy continues downwardly to be reflected by other geologicinterfaces below the interface 22, such as the interface 23. A secondreflection of seismic wave energy as indicated by the ray path 47 isupwardly traveling as it impinges on the detector 19 and is the secondupwardly traveling event to be detected. There may, of course, beseveral more of such upwardly traveling seismic waves representingreflections from lower geologic strata which are not shown in FIG. 1 forclarity of explanation.

FIG. 2 is an illustration in a synthetic vertical seismic profiledisplay of receiver depth and travel time showing how the seismic eventsassociated with the ray paths in FIG. 1 would appear in a verticalseismic profile. Each of the vertically oriented traces in the profilecorresponds to the recorded electrical signal transmitted by a singledetector in the well bore and the total 51 traces are recorded signalsfrom a detector at 51 successively lower depths in the well. However, itis also to be understood, that the vertical seismic profile could beacquired with only a single generation of seismic energy from the energysource using 51 detectors in the well bore or by a series of impacts ofthe weight dropper wherein one or more detectors are successivelypositioned at greater depths in the well bore to receive the energy.

In the vertical seismic profile of FIG. 2, the downgoing events on theprofile are the directly arriving wave from the seismic energy sourceand a multiple reflected wave reverberating in the first layer of earthbelow the energy source whereas the upgoing events are the reflectionsof seismic energy from two interfaces of earth strata. These eventsappear on a trace as a sudden increase or a peak in signal amplitude andin a vertical seismic profile these amplitude changes in the traces ofthe profile are disposed as a dipping feature of the profile. It will benoted that the amplitude changes representing the downgoing arrivingwaves in the several traces appear in alignments which are dippedoppositely to the alignments of the signal amplitude changesrepresenting the arrival of upgoing reflections which phenomenon istypical of vertical seismic profiles wherein opposite directions ofseismic wave travel within the earth lead to opposite dips on thedisplay.

Since exploration by vertical seismic profiling techniques is concernedwith detection of the reflecting horizons of the different earth strata,the detection and analysis of the upgoing waves is the primary concern.It is therefore necessary, in order to improve the signal-to-noise ratioand to better distinguish the upgoing waves, to filter the collectedsignals. It is therefore desirable that the filtering process operatesto suppress the downgoing events in the vertical seismic profile.

The filtering process of this invention will be hereinafter described byconsideration of traces 10 and 11 (produced by Receivers 10 and 11,respectively) in the vertical seismic profile of FIG. 2. These traceshave been selected so that the undesired multiple and the secondreflection interfere with one another in that they add constructively onthe first trace and cancel on the second. Despite such interference, itwill nevertheless be shown that the process of this invention cancorrectly separate the two events.

In FIG. 3, the traces 10 and 11 of FIG. 2 are reproduced exactly but areplotted in horizontal orientation for purposes of explanation. Fromobservation of FIG. 3 it will be noted that the wavelet shape for thefirst two events on each trace is a trough followed by a peak. Thesecond two events, corresponding to the second reflection and themultiple in the vertical seismic profile of FIG. 2, interfere with oneanother to construct a different wave shape (trough-peak-trough) in thefirst trace (trace 10) and to perfectly cancel one another on the secondtrace (trace 11).

The first step in the process is to form two new signals from the sumand difference of the original traces 10 and 11. These new signals arerepresented in FIG. 4 by the signal traces S_(o) and (S₁ -S₂). Fromobservation of these traces, the summed or averaged trace S_(o), withrespect to wave shape, looks much like the original traces 10 and 11.However, the difference trace (S₁ -S₂) has a different wavelet shape forthe events appearing thereon in that each wavelet is approximately 90°phase shifted, and, more important, shows a change in polarity betweenthe upgoing and downgoing events. It is therefore to be noted that thefirst two events on the summed trace, one desired and the otherundesired, look identical whereas on the difference trace, with respectto these same two events, one is upside down relative to the other.

The process then requires a wave shape correction which is achieved bythe step of integrating the difference signal to obtain an integralthereof, represented in FIG. 4 as the integral trace I. An amplitudescale correction of the integral signal is then performed followed bythe step of subtracting the integrated difference signal from the summedsignal. The subtracting step in effect doubles the amplitudes of theupgoing events and cancels the downgoing events, as is readily apparentin the signal trace (S_(o) -I) shown in FIG. 5. On occasion, the arrivalof the downgoing events may be of interest and in such case, thedowngoing events may be preserved by the step of adding the integratedand summed signals, S_(o) and I, to obtain the resulting signal trace(S_(o) +I) shown in FIG. 5. For either of the traces for FIG. 5, thearrival times of the separated events are appropriate for a depthhalfway between the receiver pair. Also, the amount of residual unwantedevents on the filtered signal traces is a function of the receiverspacing and seismic wavelet.

The filtering process of this invention is ideally suited to processingvertical seismic profiles, but has potential application wherever a dipfilter is desired. It can be used whenever desired and undesired eventsare dipping in opposite directions, or can be shifted so as to appeardipping in opposite directions. For example, a surface wave may beshifted relative to reflection energy in order to suppress the surfacewave.

As previously stated, there will normally be a requirement for applyingan amplitude scale correction to the integral signal trace beforeperforming the step of subtracting the integral trace I from the sumtrace S_(o). This correction, of course, can be specified exactly if thetime separation, as might be available from an acoustic well log or fromthe vertical seismic profile first breaks, is known. Nevertheless, thescaling can effectively be achieved by power balancing the traces beforesubtraction.

A procedure whereby a time delay scaling factor can be estimated withappropriate accuracy is herein described.

In the acquisition of a vertical seismic profile, let S₁ and S₂ be thesignals detected at two adjacent levels, level 1 and level 2, in a wellbore. Also, let the signal which would have been measured at themidpoint of the adjacent levels be denoted by S_(o). If T be the timedelay of the wave traveling between the midpoint and the levels foracquisition of S₁ and S₂, then, assuming a constant velocity layer,

    S.sub.o =u(t)+d(t)                                         (1)

    S.sub.1 =u(t-T)+d(t+T)                                     (2)

    S.sub.2 =u(t+T)+d(t-T)                                     (3)

where u(t) and d(t) are the upgoing and downgoing wave fields at themidpoint level.

S₁ and S₂ are then expanded in a Taylor's series wherein, for closelyspaced receivers, terms of first order in T are retained to obtain

    S.sub.1 =u-Tu+d+Td                                         (4)

    S.sub.2 =u+Tu+d-Td                                         (5)

wherein the dot denotes differentiation with respect to t.

The average of S₁ and S₂ is therefore

    S=(S.sub.1 +S.sub.2)/2=u+d                                 (6)

The difference of S₁ and S₂ is

    S.sub.2 -S.sub.1 =2Tu-2Td                                  (7)

The integral of the difference is

    I=2T(u-d)                                                  (8)

In equation (8), the negative coefficient of d is due to the oppositedirections of travel of the two wave fields. The factor 2 comes from thedefinition of T to be the time delay between the midpoint and level 1 or2, that is, the time delay between level 1 and level 2 is 2T.

Dividing I by 2T_(o), where T_(o) is some arbitrary constant, and addingthe result to S, the following is obtained: ##EQU1## It is thereforeapparent that u and d can be determined from the combination of S and Iexpressed in equation (9). The downgoing wave field may be eliminated bysetting T_(o) =T to obtain u. Alternatively, the upgoing wave field maybe eliminated by setting T_(o) =-T to obtain d.

T can be determined from the difference in the first arrival times of awave field at the two detectors, since the difference represents thetravel time between the two detectors. This travel time divided by 2therefore equals T. However, a more flexible and automatic procedure fordetermining T is outlined below. From equations (6), (7) and (8), thepower in S and I is given by

    P.sub.s =P.sub.u +P.sub.d +2φ.sub.o (u,d)              (10)

    P.sub.I =4T.sup.2 [P.sub.u +P.sub.d- 2φ.sub.o (u,d)]   (11)

where φ_(o) (u,d) is the zero lag cross-correlation of the upgoing anddowngoing wave fields. Since the upgoing and downgoing wave fields at agiven time are uncorrelated, φ_(o) (u,d)=0. Then, by dividing equation(11) by equation (10), the following is obtained:

    4T.sup.2 =P.sub.I /P.sub.s                                 (12)

Accordingly, T which is readily obtainable from equation (12), providesan estimated value of the time delay between the two levels, whichestimate is not based on a single value, but represents an average valueof the shifts for the whole trace. This estimated value is therefore abetter estimate than can be determined from the first arrivals alone.

It is to be noted, however, that this derived estimated value of T isvalid so long as T is small enough that terms higher than first order inthe Taylor's series can be neglected. A small enough T means that thereceivers are sufficiently close together that T is small compared tothe smallest period (associated with the highest frequency) present inthe data. If T becomes a large fraction of the smallest period, then acondition similar to "cycle skipping" occurs. That is, when comparingtwo cosine waves which have a relative time shift, it is impossible todistinguish between waves shifted up greater than half a cycle and downless than half a cycle. Since the process of this invention attempts todetect these relavtive shifts, the process will fail for thosewavelengths.

From the foregoing, it is to be concluded that the filtering processherein described yields a resulting signal approximating the signalwhich would have been recorded midway between the two receivers. Ineffect, the filter process mixes two traces whereas most multichannelfilters mix several traces. This, of course, results in the loss of onetrace per group of input traces and also results in a new depthspecification. However, since there is normally less level smearing witha two-trace filter, it better preserves faults and steeply dippingevents in offset vertical seismic profiling.

FIG. 6 shows the results of applying the process of the inventiontwo-by-two to all the traces in the synthetic vertical seismic profileof FIG. 2. It is shown therein that a single pass or application of theprocess greatly enhances the upgoing events relative to the downgoingevents. In effect, the upgoing events are doubled in amplitude and thedowngoing events are so attenuated that only a small residual could benoted. A second pass would further improve the separation but normallyis not needed unless significant differences in dip occur. For example,if mode converted events are present, one pass would reject thedowngoing P-wave (compressional wave) energy and a second pass might beneeded to reject the downgoing S-wave (shear wave) energy.

A system for implementation of the filtering method described above isshown in FIG. 7. The detector signals obtained from vertically spaceddetectors in a borehole are recorded and stored in a memory 60. Thememory 60 is controlled to furnish for processing a pair of detectorsignals, S₁ and S₂, corresponding to signals from detectors at adjacentlevels. The pair of signals are also delivered to an adder 61 and asubtractor 62 for obtaining sum and difference signals, S_(o) and ((S₁-S₂), respectively. The difference signal is then applied to anintegrating circuit 63 which produces an integral signal I. The integralsignal I is then delivered to a calculator 65 which applies an amplitudescale correction to the integral signal I as determined from theequation (12) above.

The amplitude-corrected integral signal and the sum signal are deliveredto a subtractor circuit 67 wherein the amplitude-corrected integralsignal is substracted from the sum signal S_(o) to provide an outputsignal S_(o) -I_(tc) wherein the amplitudes of upgoing seismic eventsare significantly enhanced and the downgoing events are significantlyattenuated. The output signal from the subtractor 67 is then recorded inmemory 68 from which it may be applied to a recorder display device 69for display in a vertical seismic profile.

Alternatively, or in conjunction therewith, the sum signal S_(o) and theamplitude-corrected integral signal may also be delivered to an adder 71wherein they are added to preserve the downgoing events, and theresulting summation signal stored in a memory 72.

It is also to be understood that the system is adapted to process allthe signals in a vertical seismic profile such that the process isrepeatedly applied two-by-two to all the signal traces of the profile toobtain an improved vertical seismic profile in accordance with theinvention. The system can be used with either analog or digital means ofdata processing.

An important consideration is the response of the filter to more thanone dip. Accordingly, it will herein be shown that the time scale factorwhich is chosen to eliminate a particular downgoing event alsoattenuates similar downgoing events and enhances all upgoing events. Inthis respect, it is to be noted that the scaling factor T can be relatedto the angle of approach of the incident wave. Referring to FIG. 8,which diagrammatically illustrates the approach to a receiver of anincident wave arriving at an angle to the axis line defined by a pair ofaligned receivers, it will be seen that

    2T=ΔZ cos (θ)/V                                (13)

where ΔZ is the distance between two levels, V is the velocity of thewave in the region of the two levels, and θ is the angle between thedirection of the wave travel and the axis defined by the receiver pairat two adjacent levels. A wave traveling straight down the axiscorresponds to θ=0.sup.°.

Assuming a scaling factor 2 T_(o) is chosen to reject a downgoing waveof T_(o) such that 2 T_(o) =ΔZ cos (θ_(o))/V, then if the upgoing wavehas 2 T=ΔZ cos (θ)/V, the response curve for the filter as obtained fromequation (9) is given by

    R(θ, θ.sub.o)=1-T/T.sub.o =1-cos (θ)/ cos (θ.sub.o) (14)

The graph of equation (14) is shown in FIG. 9 for an incident wave whereθ_(o) =0 and in FIGS. 10 and 11 where θ_(o) =30° and 60°, respectively.In these curves, the distance from the origin corresponds to R(θ, θ_(o))and the beam pattern polar plots indicate amplitude by circles ofsuccessively greater radius as a function of incident angle indicated byradial lines. In each of the plots, the vertical axis corresponds towell bore geophone alignment and the arrows indicate wave direction usedfor time scaling. In each of FIGS. 9, 10 and 11, the curve forR(θ,θ_(o)) traces the filter response for seismic wave events arrivingfrom all other directions.

It will be noted from FIG. 9, wherein θ_(o) =0°, that a wave approachingthe axis of the receiver pair at an angle of 0° as represented by theupper arrow is cancelled exactly, with the response curve depicting anamplitude of zero. Also, it is to be noted that a wave, such as areflected wave, which approaches the receiver pair at an angle of 180°as represented by the lower arrow is enhanced by a factor of 2.Similarly, a wave event which approaches the receiver pair at an angleof 90°, i.e. broadside to the axis of the receiver pair, arrives at bothreceivers at the same time and is passed exactly, the amplitude beingrepresented equal to 1.

Referring to FIGS. 10 and 11, the upper arrows might typically representthe direct arrivals of seismic waves from an offset seismic wave sourceand the lower arrows, a reflected wave from a horizontal substratum. Itwill be observed that the direction of exact cancellation is such thatit is always at θ_(o) and the magnitude of the response curve for a wavearriving at 180°, R(180°-θ_(o), θ_(o)), is always 2. From observation ofeach of the curves of FIGS. 9, 10 and 11, it will be noted that waveswhich approach the receiver array from below are always enhanced (R>1),while waves which approach the array in a wide band around 0° are alwaysreduced (R<1).

It is to be noted, therefore, that the two-trace filter of thisinvention has a good rejection response over a wide range of dip angles.It is particularly effective when the number of traces is small and fordip moveouts that are not linear, as in offset vertical seismicprofiling. However, if several different dips are to be rejected, asecond pass of the filter will prove advantageous.

Applications have shown the two-trace directional filtering process ofthe invention to be tolerant of poor signal-to-noise ratios and will notproduce artificial alignments like some harshly applied filters.However, since the process will enhance low frequencies relative tohighs, it is generally advisable that a band-pass filter and/or spectralbalancing operator be subsequently applied. Also, since in theprocessing of vertical seismic profiles, the invention does not requirefirst break time picks to accomplish separation of the upgoing anddowngoing events, the process can be applied at an earlier stage thanother dip filters.

It is not a requirement of the invention that receiver spacing must beuniform, although the spacing must be small enough not to aliasfrequencies of interest. If the spacing selected is too large comparedto a wavelength of seismic energy, then wavelet distortion will resultwhich is true, in general, for all dip filters. While the filter processof the present invention is useful for any wavelengths which areunaliased, the filter process is preferably used with about half thenormal range of spacing, i.e., best results are achieved with spacingsless than a quarter of the shortest wavelength. Successful applicationsof the process have been achieved with vertical seismic profiles whereinthe level spacings are between 10 and 125 feet. Accordingly, thetechnique can be used effectively on the majority of existing verticalseismic profile data sets.

The technique of the invention also allows for large depth separationsbetween closely spaced pairs of receiver locations and consequently asignificant reduction in the total number of detector levels as comparedto most existing techniques which require a small depth spacing betweenall detector levels and oftentimes produce more levels than are needed.The larger number of detecting levels are normally associated withgreater costs in service charges and rig time. Furthermore, since it ispossible to practice the invention using a ten foot detector levelspacing, it also becomes possible to place the receiver pair in the sametool, thereby allowing even more acquisition flexibility and furtherpossibilities in reducing costs.

From the foregoing description of the invention, it is to be appreciatedthat the two-trace filter process of this invention has far more generalapplications than existing techniques. There are many potentialadvantages of the two-trace filter which lie in the less restrictiveassumptions imposed on acquisition geometry and structural complexity ofthe subsurface geology, such that potential applications are to be foundwherever a dip filter is desired.

It is also to be understood that alternative techniques in performingthe various method steps of the invention may be used as are apparent tothose skilled in the art, without departing from the scope and spirit ofthe invention as defined in the appended claims.

We claim:
 1. A method of seismic geophysical surveying wherein a seismicenergy source positioned at or near the earth surface is adapted togenerate seismic wave energy which is detectable by seismic detectors invertical spaced array in a borehole and the electrical signals generatedby the seismic detectors in response thereto are processed fordiscriminating the seismic events which are upward traveling as theyarrive at the detectors from those which are downward traveling as theyarrive at the detectors, said method comprising the steps of:(a)generating seismic waves in the earth at a given location, (b) detectingthe resultant seismic waves at a plurality of vertically spaced levelsin a borehole penetrating earth formations below the energy source andgenerating representative electrical signals in response thereto bymeans of detector transducers positioned in the borehole at each saidlevel, (c) combining a pair of detector signals from a pair of detectorsat adjacent levels in the borehole to form a sum signal, (d) subtractingthe signal from the lower detector of the pair from the signal of theother detector of the pair to form a difference signal, (e) integratingthe difference signal to form an integral signal, (f) applying anestimated amplitude scale correction to the integral signal to form aresulting signal which is an approximate representation of a detectorsignal from a detector located midway between said pair of detectors,and (g) subtracting the amplitude corrected signal from said sum signalto form a modified filtered signal wherein the amplitudes of the seismicwave events which are upwardly traveling as they arrive at the detectorsare increased and the seismic wave events which are downwardly travelingas they arrive at the detectors are attenuated.
 2. A method as recitedin claim 1 wherein the seismic energy source is offset from theborehole.
 3. A method as recited in claim 1 wherein the seismic waveenergy generated by the seismic energy source is detected by verticallyspaced pairs of seismic detectors located at successively lower depthsin the borehole and the steps of the method are successively applied tothe signals of each said pair.
 4. A method as recited in claim 1 whereinthe electrical signals from the plurality of detectors are firstrecorded in aligned array in order of detector depth to form a verticalseismic profile prior to the step of combining a pair of detectorsignals.
 5. A method as recited in claim 3 wherein the filtered signalsfrom the processed pairs of detector signals are recorded in the orderof their successively greater depths to form a filtered vertical seismicprofile.
 6. A method of seismic geophysical surveying wherein a seismicenergy source positioned at or near the earth surface is adapted togenerate seismic wave energy which is detectable by seismic detectors invertical spaced array in a borehole and the electrical signals generatedby the seismic detectors in response thereto are processed fordiscriminating the seismic events which are upward traveling as theyarrive at the detectors from those which are downward traveling as theyarrive at the detectors, said method comprising the steps of:(a)generating seismic waves in the earth at a given location, (b) detectingthe resultant seismic waves at a plurality of vertically spaced levelsin a borehole penetrating earth formations below the energy source andgenerating representative electrical signals in response thereto bymeans of detector transducers positioned in the borehole at each saidlevel, (c) combining a pair of detector signals from a pair of detectorsat adjacent levels in the borehole to form a sum signal, (d) subtractingthe signal from the lower detector of the pair from the signal of theother detector of the pair to form a difference signal, (e) integratingthe difference signal to form an integral signal, (f) applying anestimated amplitude scale correction to the integral signal to form aresulting signal which is an approximate representation of a detectorsignal from a detector located midway between said pair of detectors,and (g) adding the amplitude corrected signal to said sum signal to forma filtered signal wherein the seismic wave events which are downwardlytraveling as they arrive at the detectors are preserved.
 7. A method asrecited in claim 6 wherein the seismic energy source is offset from theborehole.
 8. A method as recited in claim 6 wherein the seismic waveenergy generated by the seismic energy source is detected by verticallyspaced pairs of seismic detectors located at successively lower depthsin the borehole and the steps of the method are successively applied tothe signals of each said pair.
 9. A method as recited in claim 8 whereinthe filtered signals from said successive pairs of detector signals arerecorded in the order of their successively greater depths to form afiltered vertical seismic profile.
 10. In a method of seismicgeophysical exploration by the vertical seismic profile techniquewherein the seismic energy generated by a seismic energy source isdetected by seismic detectors in vertically spaced array in a boreholeand the representative electrical signals generated by the detectors inresponse thereto are recorded in aligned array in the order of detectordepth to form a vertical seismic profile wherein seismic events whichare upwardly traveling as they arrive at the detectors are separatedfrom downwardly traveling events as they arrive at the detectors, saidmethod comprising the steps of:(a) combining a pair of the recordeddetector signals from a pair of detectors at adjacent levels in theborehole to form a sum signal, (b) subtracting the signal from the lowerdetector of the pair from the signal of the other detector of the pairto form a difference signal, (c) integrating the difference signal toform an integral signal, (d) calculating an estimated amplitude scalecorrection for application to the integral signal to form a resultingsignal representative of a signal from a detector located between saidpair of detectors, (e) subtracting the amplitude corrected signal fromsaid sum signal to form a filtered signal wherein the upwardly travelingseismic wave events arriving at the detectors are discriminated from thedownwardly traveling seismic wave events, (f) repeating each of theforegoing steps to successive pairs of signals for all the signals ofthe vertical seismic profile, and (g) recording the successively formedfiltered signals in a vertical seismic profile.